How does Blender decide in which window it shows the render
By default it picks the largest area, unless an image editor already exists.

You can alter this behavior by setting the Display option in the render settings:




Keep UI

Does not change the UI. The render will not be automatically shown.
New Window

Opens a separate window containing only an image editor  showing the render.
Image Editor (default)

Renders into an image editor. Turns the largest area into an image editor if one doesn't exist.
Full Screen

Replaces the UI with a full screen image editor showing the render.